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Unformatted text preview: as the alleles
Three possible diploid genotypes
AA, Aa, aa Frequency of allele A is called p
Frequency of allele a is called q
p+q=1
(note: we could have called a=p and A=q, no
difference!) HardyWeinberg Equilibrium
Principle
Principle
The General Case:
Let gametes make zygotes:
Four combinations
A + A = AA
p X p = p2
A + a = Aa
p X q = pq
a + A = aA
q X p = qp
a + a = aa
q X q = q2
p2 + 2pq + q2 = 1
Genotype frequencies in HardyWeinberg
Equilibrium HardyWeinberg Equilibrium
Principle
Principle
Two fundamental conclusions:
Conclusion 1: the allele frequencies in a
population will not change, generation after
generation (given our assumptions)
Conclusion 2: if the allele frequencies in a
population are given by p and q, the genotype
frequencies will be given by p2, 2pq, and q2 HardyWeinberg Equilibrium
Principle
Principle
Why do we use HardyWeinberg
Equilibrium Principle?
• Shows evolution is not happening
• Gives specific set of testable
assumptions
• If an assumption is violated, the
Conclusions do not hold
• Is a null model with which to test for
evolution!!!! The HardyWeinberg
principle
Given certain assumptions, whatever the
initial genotype frequencies for two
autosomal alleles may be, after one
generation of random mating, the
genotype frequencies will be p2:2pq:q2,
and both the genotype frequencies and
the allele frequencies will remain
constant in succeeding generations. HWE in Action…
HWE
p +q=1
(p + q)2 = 12
p2 + 2pq + q2 = 1
f(A)
f(a) f(A)
f(AA) = f(A) x f(A)
f(aA) = f(a) x f(A) p2 = f(AA)
pq + pq = 2pq = f(Aa)
q2 = f(aa) f(a)
f(Aa) = f(A) x f(a)
f(aa) = f(a) x f(a) What is HWE good for?
What
Estimations of Allele or Genotype Frequencies:
• Predicting genotype frequencies given allele
frequencies
• Genotypes will approximate a binomial distribution
– (p + q)2 = 1 after 1 generation of random
mating.
• If we know the allele frequencies in generation 1,
we can predict the genotype frequencies in
generation 2.
• Allele and genotype frequencies will not change as
long as the assumptions are met. For example:
For
Generation 1: – f(AA) = 0.2, f(Aa) = 0.8, f(aa) = 0.0
What are the genotype frequencies in generation 2?
First, find p and q:
– p = 0.2 + (0.8 / 2) = 0.6
– q = 0.0 + (0.8 / 2) = 0.4
Generation 2: – F(AA) = p2 = 0.36
– F(Aa) = 2pq = 0.48
– F(aa) = q2 = 0.16 Another example:
Another
Generation 1: – f(AA) = 0.5, f(Aa) = 0.2, f(aa) = 0.3
What are the genotype frequencies in generation 2?
First, find p and q:
– p = 0.5 + (0.2 / 2) = 0.6
– q = 0.3 + (0.2 / 2) = 0.4
Generation 2: – F(AA) = p2 = 0.36
– F(Aa) = 2pq = 0.48
– F(aa) = q2 = 0.16 Did you notice?
Did
We started with different genotype
frequencies in each example, but the
same allele frequencies (p & q).
We ended (generation 2) with the
same genotype frequencies in both
examples.
If all of the assumptions are met, what
will be the genotype frequencies in
generation 10? What else is HWE good
for?
for?
Null hypothesis: – H0: th...
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 Fall '13

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